Simplify the expression. $(5p^{4}-6p^{3}+4p^{2})(3p^{4}-7p^{3})$
Solution: First use the distributive property. $ 5 p^4 (3 p^4) + 5 p^4 (-7 p^3) - 6 p^3 (3 p^4) - 6 p^3 (-7 p^3) + 4 p^2 (3 p^4) + 4 p^2 (-7 p^3) $ Simplify. $ 15p^{8} - 35p^{7} - 18p^{7} + 42p^{6} + 12p^{6} - 28p^{5} $ $15p^{8}-53p^{7}+54p^{6}-28p^{5}$ Identify like terms. $ { 15p^{8}} \color{#DF0030} {- 35p^{7}} \color{#DF0030} {- 18p^{7}} {+ 42p^{6}} {+ 12p^{6}} {- 28p^{5}} $ Add the coefficients. $ { 15p^{8}} \color{#DF0030} { -53p^{7}} {+ 54p^{6}} { -28p^{5}} $